   Chapter 4.3, Problem 29E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 1 4 2 + x 2 x d x

To determine

To evaluate:

142+x2x dx

Explanation

1) Concept:

i) The Fundamental Theorem of Calculus: Suppose  f is continuous on [a, b], then

abfxdx=Fb-F(a), where F is antiderivative of  f, that is F'=f.

ii) Separate out the integration and then use antiderivative of each term

2) Calculation:

142+x2x dx

After separating the denominator, the above integration becomes

14( 2x+ x2x )

By separating the integration,

142xdx+14x2xdx

Take the inverse of the denominator to simplify the equation

142·x-12dx+ 14x2-12 dx

By using the antiderivative of each term,

2x1/21/2

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